Question: A city is experimenting with an additive to the water with the objective of decreasing tooth decay. Over a ten year period, records have been kept on pounds of the chemical put into the water system and the number of children twelve or under who were cavity free that year.
(a) Show that there is a significant linear correlation between number of pounds of the chemical, and the number of children who were cavity free.
(b) Determine the equation of the regression line.
(c) Estimate the percentage of children who were cavity free that is explained by the chemical added to the water supply.
(d) Predict with a 95% confidence level how many children are likely to be cavity free if 650 pounds are used. Write the prediction interval for this estimate.